Related papers: A formula to evaluate type A webs and link polynom…
We extend the construction of the DAHA-Jones polynomials for any reduced root systems and DAHA-superpolynomials in type A from the iterated torus knots (our previous paper) to links, including arbitrary algebraic links. Such a passage…
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…
For a virtual knot $K$ and an integer $r$ with $r\geq2$, we introduce a method of constructing an $r$-component virtual link $L(K;r)$, which we call the $r$-multiplexing of $K$. Every invariant of $L(K;r)$ is an invariant of $K$. We give a…
The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded…
We discuss the problem on the connectedness of various webs of lattice polytopes by introducing a geometric point of view from the toric Mori theory. To this end, we provide a combinatorial description of toric Sarkisov links in terms of…
We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their…
We derive new formulas for the Jones polynomial and the Kauffman bracket polynomial of a rational link represented by a standard diagram that is not necessarily alternating. These formulas generalize the results of Qazaqzeh, Yasein, and…
The contents of this 98-page paper have been subsumed into the 191-page paper "A colored sl(N)-homology for links in S^3" (arXiv:0907.0695v1 [math.GT]), in which we further develop the theory and use it to construct a colored link homology.
In this article we consider the exterior power and the symmetric tensors of the polynomial ring in one variable. The structure of an associative semigraded algebra of this polynomial ring induces on the symmetric tensors the structure of an…
Using the band representation of the 3-strand braid group, it is shown that the genus of 3-braid links can be read off their skein polynomial. Some applications are given, in particular a simple proof of Morton's conjectured inequality and…
A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…
In this paper we construct invariants of 3-manifolds "\`a la Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories. We give concrete examples of such categories which lead to a family of 3-manifold invariants…
We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and…
The evaluation of web pages against a query is the pivot around which the Information Retrieval domain revolves around. The context sensitive, semantic evaluation of web pages is a non-trivial problem which needs to be addressed…
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and…
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete…
We prove a conjecture of Rozansky's concerning his categorification of the tail of the colored Jones polynomial for an $A$-adequate link. We show that the tail homology groups he constructs are trivial for non $A$-adequate links.
We study the form of the Turaev-Viro partition function Z(M) for different 3-manifolds with boundary. We show that for $S^2$ boundaries Z(M) factorizes into a term which contains the boundary dependence and another which depends only on the…
In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…
A formula for the Arf invariant of a link is given in terms of the singularities of an immersed surface bounded by the link. This is applied to study the computational complexity of quantum invariants of 3--manifolds.